LMFDB - Embedded newform 350.4.c.b.99.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [350,4,Mod(99,350)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(350, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([1, 0]))

N = Newforms(chi, 4, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("350.99");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 350 = 2 \cdot 5^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	350.c (of order $2$, degree $1$, not minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$20.6506685020$
Analytic rank:	$0$
Dimension:	$2$
Coefficient field:	$\Q(i)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} + 1 $ x^2 + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 14)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			99.1
Root			$-1.00000i$ of defining polynomial
Character	$\chi$	$=$	350.99
Dual form			350.4.c.b.99.2

$q$-expansion

comment: q-expansion

sage: f.q_expansion() # note that sage often uses an isomorphic number field

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.00000i q^{2} -8.00000i q^{3} -4.00000 q^{4} -16.0000 q^{6} -7.00000i q^{7} +8.00000i q^{8} -37.0000 q^{9} +O(q^{10})$	\(q-2.00000i q^{2} -8.00000i q^{3} -4.00000 q^{4} -16.0000 q^{6} -7.00000i q^{7} +8.00000i q^{8} -37.0000 q^{9} -28.0000 q^{11} +32.0000i q^{12} -18.0000i q^{13} -14.0000 q^{14} +16.0000 q^{16} +74.0000i q^{17} +74.0000i q^{18} -80.0000 q^{19} -56.0000 q^{21} +56.0000i q^{22} +112.000i q^{23} +64.0000 q^{24} -36.0000 q^{26} +80.0000i q^{27} +28.0000i q^{28} -190.000 q^{29} +72.0000 q^{31} -32.0000i q^{32} +224.000i q^{33} +148.000 q^{34} +148.000 q^{36} -346.000i q^{37} +160.000i q^{38} -144.000 q^{39} +162.000 q^{41} +112.000i q^{42} +412.000i q^{43} +112.000 q^{44} +224.000 q^{46} +24.0000i q^{47} -128.000i q^{48} -49.0000 q^{49} +592.000 q^{51} +72.0000i q^{52} -318.000i q^{53} +160.000 q^{54} +56.0000 q^{56} +640.000i q^{57} +380.000i q^{58} +200.000 q^{59} -198.000 q^{61} -144.000i q^{62} +259.000i q^{63} -64.0000 q^{64} +448.000 q^{66} -716.000i q^{67} -296.000i q^{68} +896.000 q^{69} +392.000 q^{71} -296.000i q^{72} -538.000i q^{73} -692.000 q^{74} +320.000 q^{76} +196.000i q^{77} +288.000i q^{78} -240.000 q^{79} -359.000 q^{81} -324.000i q^{82} +1072.00i q^{83} +224.000 q^{84} +824.000 q^{86} +1520.00i q^{87} -224.000i q^{88} -810.000 q^{89} -126.000 q^{91} -448.000i q^{92} -576.000i q^{93} +48.0000 q^{94} -256.000 q^{96} +1354.00i q^{97} +98.0000i q^{98} +1036.00 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q - 8 q^{4} - 32 q^{6} - 74 q^{9}+O(q^{10}) $ 2 * q - 8 * q^4 - 32 * q^6 - 74 * q^9	$ 2 q - 8 q^{4} - 32 q^{6} - 74 q^{9} - 56 q^{11} - 28 q^{14} + 32 q^{16} - 160 q^{19} - 112 q^{21} + 128 q^{24} - 72 q^{26} - 380 q^{29} + 144 q^{31} + 296 q^{34} + 296 q^{36} - 288 q^{39} + 324 q^{41} + 224 q^{44} + 448 q^{46} - 98 q^{49} + 1184 q^{51} + 320 q^{54} + 112 q^{56} + 400 q^{59} - 396 q^{61} - 128 q^{64} + 896 q^{66} + 1792 q^{69} + 784 q^{71} - 1384 q^{74} + 640 q^{76} - 480 q^{79} - 718 q^{81} + 448 q^{84} + 1648 q^{86} - 1620 q^{89} - 252 q^{91} + 96 q^{94} - 512 q^{96} + 2072 q^{99}+O(q^{100}) $ 2 * q - 8 * q^4 - 32 * q^6 - 74 * q^9 - 56 * q^11 - 28 * q^14 + 32 * q^16 - 160 * q^19 - 112 * q^21 + 128 * q^24 - 72 * q^26 - 380 * q^29 + 144 * q^31 + 296 * q^34 + 296 * q^36 - 288 * q^39 + 324 * q^41 + 224 * q^44 + 448 * q^46 - 98 * q^49 + 1184 * q^51 + 320 * q^54 + 112 * q^56 + 400 * q^59 - 396 * q^61 - 128 * q^64 + 896 * q^66 + 1792 * q^69 + 784 * q^71 - 1384 * q^74 + 640 * q^76 - 480 * q^79 - 718 * q^81 + 448 * q^84 + 1648 * q^86 - 1620 * q^89 - 252 * q^91 + 96 * q^94 - 512 * q^96 + 2072 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/350\mathbb{Z}\right)^\times$.

$n$	$101$	$127$
$\chi(n)$	$1$	$-1$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$	$a_n / n^{(k-1)/2}$	$ \alpha_n $			$ \theta_n $
$p$	$a_p$	$a_p / p^{(k-1)/2}$	$ \alpha_p$			$ \theta_p $

$2$	− 2.00000i	− 0.707107i
$2$	− 2.00000i	− 0.707107i
$3$	− 8.00000i	− 1.53960i	−0.638285	−	0.769800i	$-0.720356\pi$
$3$	− 8.00000i	− 1.53960i	0.638285	−	0.769800i	$-0.279644\pi$
$4$	−4.00000	−0.500000
$5$	0	0
$5$	0	0
$6$	−16.0000	−1.08866
$7$	− 7.00000i	− 0.377964i
$7$	− 7.00000i	− 0.377964i
$8$	8.00000i	0.353553i
$9$	−37.0000	−1.37037
$10$	0	0
$11$	−28.0000	−0.767483	−0.383742	−	0.923440i	$-0.625365\pi$
$11$	−28.0000	−0.767483	−0.383742	+	0.923440i	$0.625365\pi$
$12$	32.0000i	0.769800i
$13$	− 18.0000i	− 0.384023i	−0.981393	−	0.192012i	$-0.938499\pi$
$13$	− 18.0000i	− 0.384023i	0.981393	−	0.192012i	$-0.0615011\pi$
$14$	−14.0000	−0.267261
$15$	0	0
$16$	16.0000	0.250000
$17$	74.0000i	1.05574i	0.849324	+	0.527872i	$0.177010\pi$
$17$	74.0000i	1.05574i	−0.849324	+	0.527872i	$0.822990\pi$
$18$	74.0000i	0.968998i
$19$	−80.0000	−0.965961	−0.482980	−	0.875631i	$-0.660446\pi$
$19$	−80.0000	−0.965961	−0.482980	+	0.875631i	$0.660446\pi$
$20$	0	0
$21$	−56.0000	−0.581914
$22$	56.0000i	0.542693i
$23$	112.000i	1.01537i	0.861541	+	0.507687i	$0.169499\pi$
$23$	112.000i	1.01537i	−0.861541	+	0.507687i	$0.830501\pi$
$24$	64.0000	0.544331
$25$	0	0
$26$	−36.0000	−0.271545
$27$	80.0000i	0.570222i
$28$	28.0000i	0.188982i
$29$	−190.000	−1.21662	−0.608312	−	0.793698i	$-0.708153\pi$
$29$	−190.000	−1.21662	−0.608312	+	0.793698i	$0.708153\pi$
$30$	0	0
$31$	72.0000	0.417148	0.208574	−	0.978007i	$-0.433118\pi$
$31$	72.0000	0.417148	0.208574	+	0.978007i	$0.433118\pi$
$32$	− 32.0000i	− 0.176777i
$33$	224.000i	1.18162i
$34$	148.000	0.746523
$35$	0	0
$36$	148.000	0.685185
$37$	− 346.000i	− 1.53735i	−0.639638	−	0.768676i	$-0.720916\pi$
$37$	− 346.000i	− 1.53735i	0.639638	−	0.768676i	$-0.279084\pi$
$38$	160.000i	0.683038i
$39$	−144.000	−0.591242
$40$	0	0
$41$	162.000	0.617077	0.308538	−	0.951212i	$-0.400160\pi$
$41$	162.000	0.617077	0.308538	+	0.951212i	$0.400160\pi$
$42$	112.000i	0.411476i
$43$	412.000i	1.46115i	0.682833	+	0.730575i	$0.260748\pi$
$43$	412.000i	1.46115i	−0.682833	+	0.730575i	$0.739252\pi$
$44$	112.000	0.383742
$45$	0	0
$46$	224.000	0.717978
$47$	24.0000i	0.0744843i	0.999306	+	0.0372421i	$0.0118573\pi$
$47$	24.0000i	0.0744843i	−0.999306	+	0.0372421i	$0.988143\pi$
$48$	− 128.000i	− 0.384900i
$49$	−49.0000	−0.142857
$50$	0	0
$51$	592.000	1.62542
$52$	72.0000i	0.192012i
$53$	− 318.000i	− 0.824163i	−0.911147	−	0.412082i	$-0.864802\pi$
$53$	− 318.000i	− 0.824163i	0.911147	−	0.412082i	$-0.135198\pi$
$54$	160.000	0.403208
$55$	0	0
$56$	56.0000	0.133631
$57$	640.000i	1.48719i
$58$	380.000i	0.860284i
$59$	200.000	0.441318	0.220659	−	0.975351i	$-0.429179\pi$
$59$	200.000	0.441318	0.220659	+	0.975351i	$0.429179\pi$
$60$	0	0
$61$	−198.000	−0.415595	−0.207798	−	0.978172i	$-0.566630\pi$
$61$	−198.000	−0.415595	−0.207798	+	0.978172i	$0.566630\pi$
$62$	− 144.000i	− 0.294968i
$63$	259.000i	0.517951i
$64$	−64.0000	−0.125000
$65$	0	0
$66$	448.000	0.835530
$67$	− 716.000i	− 1.30557i	−0.757542	−	0.652786i	$-0.773600\pi$
$67$	− 716.000i	− 1.30557i	0.757542	−	0.652786i	$-0.226400\pi$
$68$	− 296.000i	− 0.527872i
$69$	896.000	1.56327
$70$	0	0
$71$	392.000	0.655237	0.327619	−	0.944810i	$-0.393754\pi$
$71$	392.000	0.655237	0.327619	+	0.944810i	$0.393754\pi$
$72$	− 296.000i	− 0.484499i
$73$	− 538.000i	− 0.862577i	−0.902214	−	0.431289i	$-0.858059\pi$
$73$	− 538.000i	− 0.862577i	0.902214	−	0.431289i	$-0.141941\pi$
$74$	−692.000	−1.08707
$75$	0	0
$76$	320.000	0.482980
$77$	196.000i	0.290081i
$78$	288.000i	0.418072i
$79$	−240.000	−0.341799	−0.170899	−	0.985288i	$-0.554667\pi$
$79$	−240.000	−0.341799	−0.170899	+	0.985288i	$0.554667\pi$
$80$	0	0
$81$	−359.000	−0.492455
$82$	− 324.000i	− 0.436339i
$83$	1072.00i	1.41768i	0.705370	+	0.708839i	$0.250781\pi$
$83$	1072.00i	1.41768i	−0.705370	+	0.708839i	$0.749219\pi$
$84$	224.000	0.290957
$85$	0	0
$86$	824.000	1.03319
$87$	1520.00i	1.87312i
$88$	− 224.000i	− 0.271346i
$89$	−810.000	−0.964717	−0.482359	−	0.875974i	$-0.660220\pi$
$89$	−810.000	−0.964717	−0.482359	+	0.875974i	$0.660220\pi$
$90$	0	0
$91$	−126.000	−0.145147
$92$	− 448.000i	− 0.507687i
$93$	− 576.000i	− 0.642241i
$94$	48.0000	0.0526683
$95$	0	0
$96$	−256.000	−0.272166
$97$	1354.00i	1.41730i	0.705561	+	0.708649i	$0.250695\pi$
$97$	1354.00i	1.41730i	−0.705561	+	0.708649i	$0.749305\pi$
$98$	98.0000i	0.101015i
$99$	1036.00	1.05174
$100$	0	0
$101$	−1358.00	−1.33788	−0.668941	−	0.743316i	$-0.733252\pi$
$101$	−1358.00	−1.33788	−0.668941	+	0.743316i	$0.733252\pi$
$102$	− 1184.00i	− 1.14935i
$103$	832.000i	0.795916i	0.917404	+	0.397958i	$0.130281\pi$
$103$	832.000i	0.795916i	−0.917404	+	0.397958i	$0.869719\pi$
$104$	144.000	0.135773
$105$	0	0
$106$	−636.000	−0.582772
$107$	444.000i	0.401150i	0.979678	+	0.200575i	$0.0642811\pi$
$107$	444.000i	0.401150i	−0.979678	+	0.200575i	$0.935719\pi$
$108$	− 320.000i	− 0.285111i
$109$	−1870.00	−1.64324	−0.821622	−	0.570033i	$-0.806930\pi$
$109$	−1870.00	−1.64324	−0.821622	+	0.570033i	$0.806930\pi$
$110$	0	0
$111$	−2768.00	−2.36691
$112$	− 112.000i	− 0.0944911i
$113$	− 1378.00i	− 1.14718i	−0.819143	−	0.573590i	$-0.805550\pi$
$113$	− 1378.00i	− 1.14718i	0.819143	−	0.573590i	$-0.194450\pi$
$114$	1280.00	1.05161
$115$	0	0
$116$	760.000	0.608312
$117$	666.000i	0.526254i
$118$	− 400.000i	− 0.312059i
$119$	518.000	0.399033
$120$	0	0
$121$	−547.000	−0.410969
$122$	396.000i	0.293870i
$123$	− 1296.00i	− 0.950052i
$124$	−288.000	−0.208574
$125$	0	0
$126$	518.000	0.366247
$127$	1944.00i	1.35828i	0.734007	+	0.679142i	$0.237648\pi$
$127$	1944.00i	1.35828i	−0.734007	+	0.679142i	$0.762352\pi$
$128$	128.000i	0.0883883i
$129$	3296.00	2.24959
$130$	0	0
$131$	−848.000	−0.565573	−0.282787	−	0.959183i	$-0.591259\pi$
$131$	−848.000	−0.565573	−0.282787	+	0.959183i	$0.591259\pi$
$132$	− 896.000i	− 0.590809i
$133$	560.000i	0.365099i
$134$	−1432.00	−0.923179
$135$	0	0
$136$	−592.000	−0.373262
$137$	− 2966.00i	− 1.84965i	−0.380389	−	0.924827i	$-0.624210\pi$
$137$	− 2966.00i	− 1.84965i	0.380389	−	0.924827i	$-0.375790\pi$
$138$	− 1792.00i	− 1.10540i
$139$	−2800.00	−1.70858	−0.854291	−	0.519795i	$-0.826008\pi$
$139$	−2800.00	−1.70858	−0.854291	+	0.519795i	$0.826008\pi$
$140$	0	0
$141$	192.000	0.114676
$142$	− 784.000i	− 0.463323i
$143$	504.000i	0.294731i
$144$	−592.000	−0.342593
$145$	0	0
$146$	−1076.00	−0.609934
$147$	392.000i	0.219943i
$148$	1384.00i	0.768676i
$149$	−510.000	−0.280408	−0.140204	−	0.990123i	$-0.544776\pi$
$149$	−510.000	−0.280408	−0.140204	+	0.990123i	$0.544776\pi$
$150$	0	0
$151$	592.000	0.319048	0.159524	−	0.987194i	$-0.449004\pi$
$151$	592.000	0.319048	0.159524	+	0.987194i	$0.449004\pi$
$152$	− 640.000i	− 0.341519i
$153$	− 2738.00i	− 1.44676i
$154$	392.000	0.205119
$155$	0	0
$156$	576.000	0.295621
$157$	− 2686.00i	− 1.36539i	−0.730704	−	0.682695i	$-0.760808\pi$
$157$	− 2686.00i	− 1.36539i	0.730704	−	0.682695i	$-0.239192\pi$
$158$	480.000i	0.241688i
$159$	−2544.00	−1.26888
$160$	0	0
$161$	784.000	0.383776
$162$	718.000i	0.348219i
$163$	1012.00i	0.486294i	0.969989	+	0.243147i	$0.0781798\pi$
$163$	1012.00i	0.486294i	−0.969989	+	0.243147i	$0.921820\pi$
$164$	−648.000	−0.308538
$165$	0	0
$166$	2144.00	1.00245
$167$	544.000i	0.252072i	0.992026	+	0.126036i	$0.0402254\pi$
$167$	544.000i	0.252072i	−0.992026	+	0.126036i	$0.959775\pi$
$168$	− 448.000i	− 0.205738i
$169$	1873.00	0.852526
$170$	0	0
$171$	2960.00	1.32372
$172$	− 1648.00i	− 0.730575i
$173$	− 1858.00i	− 0.816538i	−0.912862	−	0.408269i	$-0.866132\pi$
$173$	− 1858.00i	− 0.816538i	0.912862	−	0.408269i	$-0.133868\pi$
$174$	3040.00	1.32449
$175$	0	0
$176$	−448.000	−0.191871
$177$	− 1600.00i	− 0.679454i
$178$	1620.00i	0.682158i
$179$	300.000	0.125268	0.0626342	−	0.998037i	$-0.480050\pi$
$179$	300.000	0.125268	0.0626342	+	0.998037i	$0.480050\pi$
$180$	0	0
$181$	−2358.00	−0.968336	−0.484168	−	0.874975i	$-0.660878\pi$
$181$	−2358.00	−0.968336	−0.484168	+	0.874975i	$0.660878\pi$
$182$	252.000i	0.102635i
$183$	1584.00i	0.639851i
$184$	−896.000	−0.358989
$185$	0	0
$186$	−1152.00	−0.454133
$187$	− 2072.00i	− 0.810265i
$188$	− 96.0000i	− 0.0372421i
$189$	560.000	0.215524
$190$	0	0
$191$	1392.00	0.527338	0.263669	−	0.964613i	$-0.415067\pi$
$191$	1392.00	0.527338	0.263669	+	0.964613i	$0.415067\pi$
$192$	512.000i	0.192450i
$193$	− 1778.00i	− 0.663126i	−0.943433	−	0.331563i	$-0.892424\pi$
$193$	− 1778.00i	− 0.663126i	0.943433	−	0.331563i	$-0.107576\pi$
$194$	2708.00	1.00218
$195$	0	0
$196$	196.000	0.0714286
$197$	1214.00i	0.439055i	0.975606	+	0.219528i	$0.0704516\pi$
$197$	1214.00i	0.439055i	−0.975606	+	0.219528i	$0.929548\pi$
$198$	− 2072.00i	− 0.743690i
$199$	−1040.00	−0.370471	−0.185235	−	0.982694i	$-0.559305\pi$
$199$	−1040.00	−0.370471	−0.185235	+	0.982694i	$0.559305\pi$
$200$	0	0
$201$	−5728.00	−2.01006
$202$	2716.00i	0.946025i
$203$	1330.00i	0.459841i
$204$	−2368.00	−0.812712
$205$	0	0
$206$	1664.00	0.562798
$207$	− 4144.00i	− 1.39144i
$208$	− 288.000i	− 0.0960058i
$209$	2240.00	0.741359
$210$	0	0
$211$	−3868.00	−1.26201	−0.631005	−	0.775779i	$-0.717357\pi$
$211$	−3868.00	−1.26201	−0.631005	+	0.775779i	$0.717357\pi$
$212$	1272.00i	0.412082i
$213$	− 3136.00i	− 1.00880i
$214$	888.000	0.283656
$215$	0	0
$216$	−640.000	−0.201604
$217$	− 504.000i	− 0.157667i
$218$	3740.00i	1.16195i
$219$	−4304.00	−1.32802
$220$	0	0
$221$	1332.00	0.405430
$222$	5536.00i	1.67366i
$223$	− 3968.00i	− 1.19156i	−0.803149	−	0.595778i	$-0.796844\pi$
$223$	− 3968.00i	− 1.19156i	0.803149	−	0.595778i	$-0.203156\pi$
$224$	−224.000	−0.0668153
$225$	0	0
$226$	−2756.00	−0.811179
$227$	− 3936.00i	− 1.15084i	−0.817857	−	0.575422i	$-0.804838\pi$
$227$	− 3936.00i	− 1.15084i	0.817857	−	0.575422i	$-0.195162\pi$
$228$	− 2560.00i	− 0.743597i
$229$	−4810.00	−1.38801	−0.694004	−	0.719971i	$-0.744155\pi$
$229$	−4810.00	−1.38801	−0.694004	+	0.719971i	$0.744155\pi$
$230$	0	0
$231$	1568.00	0.446610
$232$	− 1520.00i	− 0.430142i
$233$	2182.00i	0.613509i	0.951789	+	0.306754i	$0.0992430\pi$
$233$	2182.00i	0.613509i	−0.951789	+	0.306754i	$0.900757\pi$
$234$	1332.00	0.372118
$235$	0	0
$236$	−800.000	−0.220659
$237$	1920.00i	0.526234i
$238$	− 1036.00i	− 0.282159i
$239$	3000.00	0.811941	0.405970	−	0.913886i	$-0.366934\pi$
$239$	3000.00	0.811941	0.405970	+	0.913886i	$0.366934\pi$
$240$	0	0
$241$	2042.00	0.545796	0.272898	−	0.962043i	$-0.412018\pi$
$241$	2042.00	0.545796	0.272898	+	0.962043i	$0.412018\pi$
$242$	1094.00i	0.290599i
$243$	5032.00i	1.32841i
$244$	792.000	0.207798
$245$	0	0
$246$	−2592.00	−0.671788
$247$	1440.00i	0.370951i
$248$	576.000i	0.147484i
$249$	8576.00	2.18266
$250$	0	0
$251$	−528.000	−0.132777	−0.0663886	−	0.997794i	$-0.521148\pi$
$251$	−528.000	−0.132777	−0.0663886	+	0.997794i	$0.521148\pi$
$252$	− 1036.00i	− 0.258976i
$253$	− 3136.00i	− 0.779283i
$254$	3888.00	0.960452
$255$	0	0
$256$	256.000	0.0625000
$257$	5634.00i	1.36747i	0.729731	+	0.683734i	$0.239645\pi$
$257$	5634.00i	1.36747i	−0.729731	+	0.683734i	$0.760355\pi$
$258$	− 6592.00i	− 1.59070i
$259$	−2422.00	−0.581065
$260$	0	0
$261$	7030.00	1.66723
$262$	1696.00i	0.399921i
$263$	− 168.000i	− 0.0393891i	−0.999806	−	0.0196945i	$-0.993731\pi$
$263$	− 168.000i	− 0.0393891i	0.999806	−	0.0196945i	$-0.00626937\pi$
$264$	−1792.00	−0.417765
$265$	0	0
$266$	1120.00	0.258164
$267$	6480.00i	1.48528i
$268$	2864.00i	0.652786i
$269$	1310.00	0.296922	0.148461	−	0.988918i	$-0.452568\pi$
$269$	1310.00	0.296922	0.148461	+	0.988918i	$0.452568\pi$
$270$	0	0
$271$	−2208.00	−0.494932	−0.247466	−	0.968897i	$-0.579598\pi$
$271$	−2208.00	−0.494932	−0.247466	+	0.968897i	$0.579598\pi$
$272$	1184.00i	0.263936i
$273$	1008.00i	0.223469i
$274$	−5932.00	−1.30790
$275$	0	0
$276$	−3584.00	−0.781636
$277$	5294.00i	1.14832i	0.818742	+	0.574162i	$0.194672\pi$
$277$	5294.00i	1.14832i	−0.818742	+	0.574162i	$0.805328\pi$
$278$	5600.00i	1.20815i
$279$	−2664.00	−0.571647
$280$	0	0
$281$	3242.00	0.688262	0.344131	−	0.938922i	$-0.388174\pi$
$281$	3242.00	0.688262	0.344131	+	0.938922i	$0.388174\pi$
$282$	− 384.000i	− 0.0810882i
$283$	1592.00i	0.334398i	0.985923	+	0.167199i	$0.0534722\pi$
$283$	1592.00i	0.334398i	−0.985923	+	0.167199i	$0.946528\pi$
$284$	−1568.00	−0.327619
$285$	0	0
$286$	1008.00	0.208407
$287$	− 1134.00i	− 0.233233i
$288$	1184.00i	0.242250i
$289$	−563.000	−0.114594
$290$	0	0
$291$	10832.0	2.18207
$292$	2152.00i	0.431289i
$293$	5022.00i	1.00133i	0.865642	+	0.500663i	$0.166910\pi$
$293$	5022.00i	1.00133i	−0.865642	+	0.500663i	$0.833090\pi$
$294$	784.000	0.155523
$295$	0	0
$296$	2768.00	0.543536
$297$	− 2240.00i	− 0.437636i
$298$	1020.00i	0.198279i
$299$	2016.00	0.389927
$300$	0	0
$301$	2884.00	0.552262
$302$	− 1184.00i	− 0.225601i
$303$	10864.0i	2.05980i
$304$	−1280.00	−0.241490
$305$	0	0
$306$	−5476.00	−1.02301
$307$	− 9536.00i	− 1.77280i	−0.462924	−	0.886398i	$-0.653200\pi$
$307$	− 9536.00i	− 1.77280i	0.462924	−	0.886398i	$-0.346800\pi$
$308$	− 784.000i	− 0.145041i
$309$	6656.00	1.22539
$310$	0	0
$311$	−968.000	−0.176496	−0.0882480	−	0.996099i	$-0.528127\pi$
$311$	−968.000	−0.176496	−0.0882480	+	0.996099i	$0.528127\pi$
$312$	− 1152.00i	− 0.209036i
$313$	− 3058.00i	− 0.552231i	−0.961124	−	0.276116i	$-0.910953\pi$
$313$	− 3058.00i	− 0.552231i	0.961124	−	0.276116i	$-0.0890473\pi$
$314$	−5372.00	−0.965476
$315$	0	0
$316$	960.000	0.170899
$317$	− 4986.00i	− 0.883412i	−0.897160	−	0.441706i	$-0.854373\pi$
$317$	− 4986.00i	− 0.883412i	0.897160	−	0.441706i	$-0.145627\pi$
$318$	5088.00i	0.897235i
$319$	5320.00	0.933739
$320$	0	0
$321$	3552.00	0.617612
$322$	− 1568.00i	− 0.271370i
$323$	− 5920.00i	− 1.01981i
$324$	1436.00	0.246228
$325$	0	0
$326$	2024.00	0.343862
$327$	14960.0i	2.52994i
$328$	1296.00i	0.218170i
$329$	168.000	0.0281524
$330$	0	0
$331$	8612.00	1.43009	0.715043	−	0.699081i	$-0.246407\pi$
$331$	8612.00	1.43009	0.715043	+	0.699081i	$0.246407\pi$
$332$	− 4288.00i	− 0.708839i
$333$	12802.0i	2.10674i
$334$	1088.00	0.178242
$335$	0	0
$336$	−896.000	−0.145479
$337$	− 10206.0i	− 1.64972i	−0.565336	−	0.824861i	$-0.691253\pi$
$337$	− 10206.0i	− 1.64972i	0.565336	−	0.824861i	$-0.308747\pi$
$338$	− 3746.00i	− 0.602827i
$339$	−11024.0	−1.76620
$340$	0	0
$341$	−2016.00	−0.320154
$342$	− 5920.00i	− 0.936014i
$343$	343.000i	0.0539949i
$344$	−3296.00	−0.516594
$345$	0	0
$346$	−3716.00	−0.577380
$347$	2004.00i	0.310030i	0.987912	+	0.155015i	$0.0495426\pi$
$347$	2004.00i	0.310030i	−0.987912	+	0.155015i	$0.950457\pi$
$348$	− 6080.00i	− 0.936558i
$349$	−1330.00	−0.203992	−0.101996	−	0.994785i	$-0.532523\pi$
$349$	−1330.00	−0.203992	−0.101996	+	0.994785i	$0.532523\pi$
$350$	0	0
$351$	1440.00	0.218979
$352$	896.000i	0.135673i
$353$	− 978.000i	− 0.147461i	−0.997278	−	0.0737304i	$-0.976510\pi$
$353$	− 978.000i	− 0.147461i	0.997278	−	0.0737304i	$-0.0234904\pi$
$354$	−3200.00	−0.480447
$355$	0	0
$356$	3240.00	0.482359
$357$	− 4144.00i	− 0.614352i
$358$	− 600.000i	− 0.0885782i
$359$	9680.00	1.42309	0.711547	−	0.702638i	$-0.247995\pi$
$359$	9680.00	1.42309	0.711547	+	0.702638i	$0.247995\pi$
$360$	0	0
$361$	−459.000	−0.0669194
$362$	4716.00i	0.684717i
$363$	4376.00i	0.632728i
$364$	504.000	0.0725736
$365$	0	0
$366$	3168.00	0.452443
$367$	− 8656.00i	− 1.23117i	−0.788070	−	0.615585i	$-0.788920\pi$
$367$	− 8656.00i	− 1.23117i	0.788070	−	0.615585i	$-0.211080\pi$
$368$	1792.00i	0.253844i
$369$	−5994.00	−0.845624
$370$	0	0
$371$	−2226.00	−0.311504
$372$	2304.00i	0.321121i
$373$	− 5278.00i	− 0.732666i	−0.930484	−	0.366333i	$-0.880613\pi$
$373$	− 5278.00i	− 0.732666i	0.930484	−	0.366333i	$-0.119387\pi$
$374$	−4144.00	−0.572944
$375$	0	0
$376$	−192.000	−0.0263342
$377$	3420.00i	0.467212i
$378$	− 1120.00i	− 0.152398i
$379$	−6340.00	−0.859272	−0.429636	−	0.903002i	$-0.641358\pi$
$379$	−6340.00	−0.859272	−0.429636	+	0.903002i	$0.641358\pi$
$380$	0	0
$381$	15552.0	2.09122
$382$	− 2784.00i	− 0.372884i
$383$	6232.00i	0.831437i	0.909493	+	0.415718i	$0.136470\pi$
$383$	6232.00i	0.831437i	−0.909493	+	0.415718i	$0.863530\pi$
$384$	1024.00	0.136083
$385$	0	0
$386$	−3556.00	−0.468901
$387$	− 15244.0i	− 2.00232i
$388$	− 5416.00i	− 0.708649i
$389$	14810.0	1.93033	0.965163	−	0.261649i	$-0.0842664\pi$
$389$	14810.0	1.93033	0.965163	+	0.261649i	$0.0842664\pi$
$390$	0	0
$391$	−8288.00	−1.07197
$392$	− 392.000i	− 0.0505076i
$393$	6784.00i	0.870757i
$394$	2428.00	0.310459
$395$	0	0
$396$	−4144.00	−0.525868
$397$	5154.00i	0.651566i	0.945445	+	0.325783i	$0.105628\pi$
$397$	5154.00i	0.651566i	−0.945445	+	0.325783i	$0.894372\pi$
$398$	2080.00i	0.261962i
$399$	4480.00	0.562107
$400$	0	0
$401$	3282.00	0.408716	0.204358	−	0.978896i	$-0.434489\pi$
$401$	3282.00	0.408716	0.204358	+	0.978896i	$0.434489\pi$
$402$	11456.0i	1.42133i
$403$	− 1296.00i	− 0.160194i
$404$	5432.00	0.668941
$405$	0	0
$406$	2660.00	0.325157
$407$	9688.00i	1.17989i
$408$	4736.00i	0.574674i
$409$	−5810.00	−0.702411	−0.351205	−	0.936298i	$-0.614228\pi$
$409$	−5810.00	−0.702411	−0.351205	+	0.936298i	$0.614228\pi$
$410$	0	0
$411$	−23728.0	−2.84773
$412$	− 3328.00i	− 0.397958i
$413$	− 1400.00i	− 0.166803i
$414$	−8288.00	−0.983896
$415$	0	0
$416$	−576.000	−0.0678864
$417$	22400.0i	2.63053i
$418$	− 4480.00i	− 0.524220i
$419$	−13560.0	−1.58102	−0.790512	−	0.612446i	$-0.790186\pi$
$419$	−13560.0	−1.58102	−0.790512	+	0.612446i	$0.790186\pi$
$420$	0	0
$421$	−738.000	−0.0854345	−0.0427172	−	0.999087i	$-0.513601\pi$
$421$	−738.000	−0.0854345	−0.0427172	+	0.999087i	$0.513601\pi$
$422$	7736.00i	0.892376i
$423$	− 888.000i	− 0.102071i
$424$	2544.00	0.291386
$425$	0	0
$426$	−6272.00	−0.713332
$427$	1386.00i	0.157080i
$428$	− 1776.00i	− 0.200575i
$429$	4032.00	0.453769
$430$	0	0
$431$	1272.00	0.142158	0.0710790	−	0.997471i	$-0.477356\pi$
$431$	1272.00	0.142158	0.0710790	+	0.997471i	$0.477356\pi$
$432$	1280.00i	0.142556i
$433$	5062.00i	0.561811i	0.959735	+	0.280906i	$0.0906348\pi$
$433$	5062.00i	0.561811i	−0.959735	+	0.280906i	$0.909365\pi$
$434$	−1008.00	−0.111487
$435$	0	0
$436$	7480.00	0.821622
$437$	− 8960.00i	− 0.980812i
$438$	8608.00i	0.939055i
$439$	−5640.00	−0.613172	−0.306586	−	0.951843i	$-0.599187\pi$
$439$	−5640.00	−0.613172	−0.306586	+	0.951843i	$0.599187\pi$
$440$	0	0
$441$	1813.00	0.195767
$442$	− 2664.00i	− 0.286682i
$443$	− 13388.0i	− 1.43585i	−0.696119	−	0.717927i	$-0.745091\pi$
$443$	− 13388.0i	− 1.43585i	0.696119	−	0.717927i	$-0.254909\pi$
$444$	11072.0	1.18345
$445$	0	0
$446$	−7936.00	−0.842557
$447$	4080.00i	0.431717i
$448$	448.000i	0.0472456i
$449$	3230.00	0.339495	0.169747	−	0.985488i	$-0.445705\pi$
$449$	3230.00	0.339495	0.169747	+	0.985488i	$0.445705\pi$
$450$	0	0
$451$	−4536.00	−0.473596
$452$	5512.00i	0.573590i
$453$	− 4736.00i	− 0.491207i
$454$	−7872.00	−0.813769
$455$	0	0
$456$	−5120.00	−0.525803
$457$	− 10646.0i	− 1.08971i	−0.838529	−	0.544857i	$-0.816584\pi$
$457$	− 10646.0i	− 1.08971i	0.838529	−	0.544857i	$-0.183416\pi$
$458$	9620.00i	0.981470i
$459$	−5920.00	−0.602009
$460$	0	0
$461$	7282.00	0.735698	0.367849	−	0.929886i	$-0.380094\pi$
$461$	7282.00	0.735698	0.367849	+	0.929886i	$0.380094\pi$
$462$	− 3136.00i	− 0.315801i
$463$	− 12688.0i	− 1.27357i	−0.771043	−	0.636783i	$-0.780265\pi$
$463$	− 12688.0i	− 1.27357i	0.771043	−	0.636783i	$-0.219735\pi$
$464$	−3040.00	−0.304156
$465$	0	0
$466$	4364.00	0.433816
$467$	− 2816.00i	− 0.279034i	−0.990220	−	0.139517i	$-0.955445\pi$
$467$	− 2816.00i	− 0.279034i	0.990220	−	0.139517i	$-0.0445550\pi$
$468$	− 2664.00i	− 0.263127i
$469$	−5012.00	−0.493460
$470$	0	0
$471$	−21488.0	−2.10215
$472$	1600.00i	0.156030i
$473$	− 11536.0i	− 1.12141i
$474$	3840.00	0.372103
$475$	0	0
$476$	−2072.00	−0.199517
$477$	11766.0i	1.12941i
$478$	− 6000.00i	− 0.574129i
$479$	3160.00	0.301428	0.150714	−	0.988577i	$-0.451843\pi$
$479$	3160.00	0.301428	0.150714	+	0.988577i	$0.451843\pi$
$480$	0	0
$481$	−6228.00	−0.590379
$482$	− 4084.00i	− 0.385936i
$483$	− 6272.00i	− 0.590861i
$484$	2188.00	0.205485
$485$	0	0
$486$	10064.0	0.939326
$487$	− 14176.0i	− 1.31905i	−0.751684	−	0.659523i	$-0.770758\pi$
$487$	− 14176.0i	− 1.31905i	0.751684	−	0.659523i	$-0.229242\pi$
$488$	− 1584.00i	− 0.146935i
$489$	8096.00	0.748699
$490$	0	0
$491$	−11268.0	−1.03568	−0.517839	−	0.855478i	$-0.673263\pi$
$491$	−11268.0	−1.03568	−0.517839	+	0.855478i	$0.673263\pi$
$492$	5184.00i	0.475026i
$493$	− 14060.0i	− 1.28444i
$494$	2880.00	0.262302
$495$	0	0
$496$	1152.00	0.104287
$497$	− 2744.00i	− 0.247656i
$498$	− 17152.0i	− 1.54337i
$499$	4460.00	0.400114	0.200057	−	0.979784i	$-0.435887\pi$
$499$	4460.00	0.400114	0.200057	+	0.979784i	$0.435887\pi$
$500$	0	0
$501$	4352.00	0.388090
$502$	1056.00i	0.0938876i
$503$	1512.00i	0.134029i	0.997752	+	0.0670147i	$0.0213474\pi$
$503$	1512.00i	0.134029i	−0.997752	+	0.0670147i	$0.978653\pi$
$504$	−2072.00	−0.183123
$505$	0	0
$506$	−6272.00	−0.551036
$507$	− 14984.0i	− 1.31255i
$508$	− 7776.00i	− 0.679142i
$509$	11790.0	1.02668	0.513342	−	0.858184i	$-0.328407\pi$
$509$	11790.0	1.02668	0.513342	+	0.858184i	$0.328407\pi$
$510$	0	0
$511$	−3766.00	−0.326024
$512$	− 512.000i	− 0.0441942i
$513$	− 6400.00i	− 0.550813i
$514$	11268.0	0.966946
$515$	0	0
$516$	−13184.0	−1.12479
$517$	− 672.000i	− 0.0571654i
$518$	4844.00i	0.410875i
$519$	−14864.0	−1.25714
$520$	0	0
$521$	1362.00	0.114530	0.0572652	−	0.998359i	$-0.481762\pi$
$521$	1362.00	0.114530	0.0572652	+	0.998359i	$0.481762\pi$
$522$	− 14060.0i	− 1.17891i
$523$	− 6968.00i	− 0.582580i	−0.956635	−	0.291290i	$-0.905916\pi$
$523$	− 6968.00i	− 0.582580i	0.956635	−	0.291290i	$-0.0940845\pi$
$524$	3392.00	0.282787
$525$	0	0
$526$	−336.000	−0.0278523
$527$	5328.00i	0.440401i
$528$	3584.00i	0.295405i
$529$	−377.000	−0.0309855
$530$	0	0
$531$	−7400.00	−0.604770
$532$	− 2240.00i	− 0.182549i
$533$	− 2916.00i	− 0.236972i
$534$	12960.0	1.05025
$535$	0	0
$536$	5728.00	0.461589
$537$	− 2400.00i	− 0.192863i
$538$	− 2620.00i	− 0.209956i
$539$	1372.00	0.109640
$540$	0	0
$541$	7062.00	0.561218	0.280609	−	0.959822i	$-0.409464\pi$
$541$	7062.00	0.561218	0.280609	+	0.959822i	$0.409464\pi$
$542$	4416.00i	0.349969i
$543$	18864.0i	1.49085i
$544$	2368.00	0.186631
$545$	0	0
$546$	2016.00	0.158016
$547$	− 8196.00i	− 0.640650i	−0.947308	−	0.320325i	$-0.896208\pi$
$547$	− 8196.00i	− 0.640650i	0.947308	−	0.320325i	$-0.103792\pi$
$548$	11864.0i	0.924827i
$549$	7326.00	0.569519
$550$	0	0
$551$	15200.0	1.17521
$552$	7168.00i	0.552700i
$553$	1680.00i	0.129188i
$554$	10588.0	0.811987
$555$	0	0
$556$	11200.0	0.854291
$557$	− 7466.00i	− 0.567944i	−0.958833	−	0.283972i	$-0.908348\pi$
$557$	− 7466.00i	− 0.567944i	0.958833	−	0.283972i	$-0.0916522\pi$
$558$	5328.00i	0.404215i
$559$	7416.00	0.561115
$560$	0	0
$561$	−16576.0	−1.24749
$562$	− 6484.00i	− 0.486674i
$563$	− 24968.0i	− 1.86905i	−0.355896	−	0.934526i	$-0.615824\pi$
$563$	− 24968.0i	− 1.86905i	0.355896	−	0.934526i	$-0.384176\pi$
$564$	−768.000	−0.0573380
$565$	0	0
$566$	3184.00	0.236455
$567$	2513.00i	0.186131i
$568$	3136.00i	0.231661i
$569$	−14250.0	−1.04990	−0.524948	−	0.851134i	$-0.675915\pi$
$569$	−14250.0	−1.04990	−0.524948	+	0.851134i	$0.675915\pi$
$570$	0	0
$571$	6372.00	0.467005	0.233503	−	0.972356i	$-0.424981\pi$
$571$	6372.00	0.467005	0.233503	+	0.972356i	$0.424981\pi$
$572$	− 2016.00i	− 0.147366i
$573$	− 11136.0i	− 0.811890i
$574$	−2268.00	−0.164921
$575$	0	0
$576$	2368.00	0.171296
$577$	− 8366.00i	− 0.603607i	−0.953370	−	0.301803i	$-0.902411\pi$
$577$	− 8366.00i	− 0.603607i	0.953370	−	0.301803i	$-0.0975886\pi$
$578$	1126.00i	0.0810301i
$579$	−14224.0	−1.02095
$580$	0	0
$581$	7504.00	0.535832
$582$	− 21664.0i	− 1.54296i
$583$	8904.00i	0.632532i
$584$	4304.00	0.304967
$585$	0	0
$586$	10044.0	0.708044
$587$	20384.0i	1.43328i	0.697441	+	0.716642i	$0.254322\pi$
$587$	20384.0i	1.43328i	−0.697441	+	0.716642i	$0.745678\pi$
$588$	− 1568.00i	− 0.109971i
$589$	−5760.00	−0.402948
$590$	0	0
$591$	9712.00	0.675970
$592$	− 5536.00i	− 0.384338i
$593$	− 9378.00i	− 0.649424i	−0.945813	−	0.324712i	$-0.894733\pi$
$593$	− 9378.00i	− 0.649424i	0.945813	−	0.324712i	$-0.105267\pi$
$594$	−4480.00	−0.309456
$595$	0	0
$596$	2040.00	0.140204
$597$	8320.00i	0.570377i
$598$	− 4032.00i	− 0.275720i
$599$	9000.00	0.613907	0.306953	−	0.951725i	$-0.400690\pi$
$599$	9000.00	0.613907	0.306953	+	0.951725i	$0.400690\pi$
$600$	0	0
$601$	7562.00	0.513245	0.256623	−	0.966512i	$-0.417390\pi$
$601$	7562.00	0.513245	0.256623	+	0.966512i	$0.417390\pi$
$602$	− 5768.00i	− 0.390509i
$603$	26492.0i	1.78912i
$604$	−2368.00	−0.159524
$605$	0	0
$606$	21728.0	1.45650
$607$	− 2976.00i	− 0.198999i	−0.995038	−	0.0994993i	$-0.968276\pi$
$607$	− 2976.00i	− 0.198999i	0.995038	−	0.0994993i	$-0.0317241\pi$
$608$	2560.00i	0.170759i
$609$	10640.0	0.707971
$610$	0	0
$611$	432.000	0.0286037
$612$	10952.0i	0.723380i
$613$	− 4278.00i	− 0.281871i	−0.990019	−	0.140935i	$-0.954989\pi$
$613$	− 4278.00i	− 0.281871i	0.990019	−	0.140935i	$-0.0450110\pi$
$614$	−19072.0	−1.25356
$615$	0	0
$616$	−1568.00	−0.102559
$617$	18794.0i	1.22629i	0.789972	+	0.613143i	$0.210095\pi$
$617$	18794.0i	1.22629i	−0.789972	+	0.613143i	$0.789905\pi$
$618$	− 13312.0i	− 0.866484i
$619$	−18040.0	−1.17139	−0.585694	−	0.810532i	$-0.699178\pi$
$619$	−18040.0	−1.17139	−0.585694	+	0.810532i	$0.699178\pi$
$620$	0	0
$621$	−8960.00	−0.578989
$622$	1936.00i	0.124801i
$623$	5670.00i	0.364629i
$624$	−2304.00	−0.147811
$625$	0	0
$626$	−6116.00	−0.390486
$627$	− 17920.0i	− 1.14140i
$628$	10744.0i	0.682695i
$629$	25604.0	1.62305
$630$	0	0
$631$	−21688.0	−1.36828	−0.684141	−	0.729350i	$-0.739823\pi$
$631$	−21688.0	−1.36828	−0.684141	+	0.729350i	$0.739823\pi$
$632$	− 1920.00i	− 0.120844i
$633$	30944.0i	1.94299i
$634$	−9972.00	−0.624667
$635$	0	0
$636$	10176.0	0.634441
$637$	882.000i	0.0548605i
$638$	− 10640.0i	− 0.660253i
$639$	−14504.0	−0.897918
$640$	0	0
$641$	−10558.0	−0.650571	−0.325285	−	0.945616i	$-0.605460\pi$
$641$	−10558.0	−0.650571	−0.325285	+	0.945616i	$0.605460\pi$
$642$	− 7104.00i	− 0.436717i
$643$	26152.0i	1.60394i	0.597363	+	0.801971i	$0.296215\pi$
$643$	26152.0i	1.60394i	−0.597363	+	0.801971i	$0.703785\pi$
$644$	−3136.00	−0.191888
$645$	0	0
$646$	−11840.0	−0.721112
$647$	25584.0i	1.55458i	0.629145	+	0.777288i	$0.283405\pi$
$647$	25584.0i	1.55458i	−0.629145	+	0.777288i	$0.716595\pi$
$648$	− 2872.00i	− 0.174109i
$649$	−5600.00	−0.338705
$650$	0	0
$651$	−4032.00	−0.242744
$652$	− 4048.00i	− 0.243147i
$653$	− 15198.0i	− 0.910787i	−0.890290	−	0.455393i	$-0.849499\pi$
$653$	− 15198.0i	− 0.910787i	0.890290	−	0.455393i	$-0.150501\pi$
$654$	29920.0	1.78894
$655$	0	0
$656$	2592.00	0.154269
$657$	19906.0i	1.18205i
$658$	− 336.000i	− 0.0199068i
$659$	6100.00	0.360580	0.180290	−	0.983613i	$-0.442296\pi$
$659$	6100.00	0.360580	0.180290	+	0.983613i	$0.442296\pi$
$660$	0	0
$661$	−2318.00	−0.136399	−0.0681995	−	0.997672i	$-0.521725\pi$
$661$	−2318.00	−0.136399	−0.0681995	+	0.997672i	$0.521725\pi$
$662$	− 17224.0i	− 1.01122i
$663$	− 10656.0i	− 0.624200i
$664$	−8576.00	−0.501225
$665$	0	0
$666$	25604.0	1.48969
$667$	− 21280.0i	− 1.23533i
$668$	− 2176.00i	− 0.126036i
$669$	−31744.0	−1.83452
$670$	0	0
$671$	5544.00	0.318962
$672$	1792.00i	0.102869i
$673$	10222.0i	0.585482i	0.956192	+	0.292741i	$0.0945673\pi$
$673$	10222.0i	0.585482i	−0.956192	+	0.292741i	$0.905433\pi$
$674$	−20412.0	−1.16653
$675$	0	0
$676$	−7492.00	−0.426263
$677$	25434.0i	1.44388i	0.691955	+	0.721941i	$0.256750\pi$
$677$	25434.0i	1.44388i	−0.691955	+	0.721941i	$0.743250\pi$
$678$	22048.0i	1.24889i
$679$	9478.00	0.535688
$680$	0	0
$681$	−31488.0	−1.77184
$682$	4032.00i	0.226383i
$683$	8532.00i	0.477991i	0.971021	+	0.238996i	$0.0768181\pi$
$683$	8532.00i	0.477991i	−0.971021	+	0.238996i	$0.923182\pi$
$684$	−11840.0	−0.661862
$685$	0	0
$686$	686.000	0.0381802
$687$	38480.0i	2.13698i
$688$	6592.00i	0.365287i
$689$	−5724.00	−0.316498
$690$	0	0
$691$	20672.0	1.13806	0.569030	−	0.822317i	$-0.307319\pi$
$691$	20672.0	1.13806	0.569030	+	0.822317i	$0.307319\pi$
$692$	7432.00i	0.408269i
$693$	− 7252.00i	− 0.397519i
$694$	4008.00	0.219224
$695$	0	0
$696$	−12160.0	−0.662247
$697$	11988.0i	0.651475i
$698$	2660.00i	0.144244i
$699$	17456.0	0.944559
$700$	0	0
$701$	−21458.0	−1.15614	−0.578072	−	0.815985i	$-0.696195\pi$
$701$	−21458.0	−1.15614	−0.578072	+	0.815985i	$0.696195\pi$
$702$	− 2880.00i	− 0.154841i
$703$	27680.0i	1.48502i
$704$	1792.00	0.0959354
$705$	0	0
$706$	−1956.00	−0.104271
$707$	9506.00i	0.505672i
$708$	6400.00i	0.339727i
$709$	9850.00	0.521755	0.260878	−	0.965372i	$-0.415988\pi$
$709$	9850.00	0.521755	0.260878	+	0.965372i	$0.415988\pi$
$710$	0	0
$711$	8880.00	0.468391
$712$	− 6480.00i	− 0.341079i
$713$	8064.00i	0.423561i
$714$	−8288.00	−0.434413
$715$	0	0
$716$	−1200.00	−0.0626342
$717$	− 24000.0i	− 1.25006i
$718$	− 19360.0i	− 1.00628i
$719$	18840.0	0.977209	0.488605	−	0.872505i	$-0.337506\pi$
$719$	18840.0	0.977209	0.488605	+	0.872505i	$0.337506\pi$
$720$	0	0
$721$	5824.00	0.300828
$722$	918.000i	0.0473191i
$723$	− 16336.0i	− 0.840308i
$724$	9432.00	0.484168
$725$	0	0
$726$	8752.00	0.447407
$727$	37504.0i	1.91327i	0.291291	+	0.956634i	$0.405915\pi$
$727$	37504.0i	1.91327i	−0.291291	+	0.956634i	$0.594085\pi$
$728$	− 1008.00i	− 0.0513173i
$729$	30563.0	1.55276
$730$	0	0
$731$	−30488.0	−1.54260
$732$	− 6336.00i	− 0.319925i
$733$	− 13338.0i	− 0.672101i	−0.941844	−	0.336051i	$-0.890909\pi$
$733$	− 13338.0i	− 0.672101i	0.941844	−	0.336051i	$-0.109091\pi$
$734$	−17312.0	−0.870569
$735$	0	0
$736$	3584.00	0.179495
$737$	20048.0i	1.00200i
$738$	11988.0i	0.597946i
$739$	−17100.0	−0.851196	−0.425598	−	0.904912i	$-0.639936\pi$
$739$	−17100.0	−0.851196	−0.425598	+	0.904912i	$0.639936\pi$
$740$	0	0
$741$	11520.0	0.571117
$742$	4452.00i	0.220267i
$743$	19632.0i	0.969352i	0.874694	+	0.484676i	$0.161062\pi$
$743$	19632.0i	0.969352i	−0.874694	+	0.484676i	$0.838938\pi$
$744$	4608.00	0.227067
$745$	0	0
$746$	−10556.0	−0.518073
$747$	− 39664.0i	− 1.94274i
$748$	8288.00i	0.405133i
$749$	3108.00	0.151621
$750$	0	0
$751$	33912.0	1.64776	0.823879	−	0.566766i	$-0.191805\pi$
$751$	33912.0	1.64776	0.823879	+	0.566766i	$0.191805\pi$
$752$	384.000i	0.0186211i
$753$	4224.00i	0.204424i
$754$	6840.00	0.330369
$755$	0	0
$756$	−2240.00	−0.107762
$757$	− 31386.0i	− 1.50693i	−0.657490	−	0.753463i	$-0.728382\pi$
$757$	− 31386.0i	− 1.50693i	0.657490	−	0.753463i	$-0.271618\pi$
$758$	12680.0i	0.607597i
$759$	−25088.0	−1.19978
$760$	0	0
$761$	−34558.0	−1.64616	−0.823079	−	0.567927i	$-0.807746\pi$
$761$	−34558.0	−1.64616	−0.823079	+	0.567927i	$0.807746\pi$
$762$	− 31104.0i	− 1.47871i
$763$	13090.0i	0.621088i
$764$	−5568.00	−0.263669
$765$	0	0
$766$	12464.0	0.587915
$767$	− 3600.00i	− 0.169476i
$768$	− 2048.00i	− 0.0962250i
$769$	−39130.0	−1.83493	−0.917467	−	0.397812i	$-0.869769\pi$
$769$	−39130.0	−1.83493	−0.917467	+	0.397812i	$0.869769\pi$
$770$	0	0
$771$	45072.0	2.10535
$772$	7112.00i	0.331563i
$773$	25982.0i	1.20894i	0.796629	+	0.604468i	$0.206614\pi$
$773$	25982.0i	1.20894i	−0.796629	+	0.604468i	$0.793386\pi$
$774$	−30488.0	−1.41585
$775$	0	0
$776$	−10832.0	−0.501090
$777$	19376.0i	0.894608i
$778$	− 29620.0i	− 1.36495i
$779$	−12960.0	−0.596072
$780$	0	0
$781$	−10976.0	−0.502884
$782$	16576.0i	0.758001i
$783$	− 15200.0i	− 0.693747i
$784$	−784.000	−0.0357143
$785$	0	0
$786$	13568.0	0.615718
$787$	35424.0i	1.60448i	0.596999	+	0.802242i	$0.296360\pi$
$787$	35424.0i	1.60448i	−0.596999	+	0.802242i	$0.703640\pi$
$788$	− 4856.00i	− 0.219528i
$789$	−1344.00	−0.0606434
$790$	0	0
$791$	−9646.00	−0.433593
$792$	8288.00i	0.371845i
$793$	3564.00i	0.159598i
$794$	10308.0	0.460727
$795$	0	0
$796$	4160.00	0.185235
$797$	− 30606.0i	− 1.36025i	−0.733096	−	0.680126i	$-0.761925\pi$
$797$	− 30606.0i	− 1.36025i	0.733096	−	0.680126i	$-0.238075\pi$
$798$	− 8960.00i	− 0.397469i
$799$	−1776.00	−0.0786362
$800$	0	0
$801$	29970.0	1.32202
$802$	− 6564.00i	− 0.289006i
$803$	15064.0i	0.662014i
$804$	22912.0	1.00503
$805$	0	0
$806$	−2592.00	−0.113275
$807$	− 10480.0i	− 0.457142i
$808$	− 10864.0i	− 0.473013i
$809$	−16810.0	−0.730542	−0.365271	−	0.930901i	$-0.619024\pi$
$809$	−16810.0	−0.730542	−0.365271	+	0.930901i	$0.619024\pi$
$810$	0	0
$811$	−9368.00	−0.405616	−0.202808	−	0.979218i	$-0.565007\pi$
$811$	−9368.00	−0.405616	−0.202808	+	0.979218i	$0.565007\pi$
$812$	− 5320.00i	− 0.229920i
$813$	17664.0i	0.761997i
$814$	19376.0	0.834310
$815$	0	0
$816$	9472.00	0.406356
$817$	− 32960.0i	− 1.41141i
$818$	11620.0i	0.496679i
$819$	4662.00	0.198905
$820$	0	0
$821$	34382.0	1.46156	0.730780	−	0.682614i	$-0.239157\pi$
$821$	34382.0	1.46156	0.730780	+	0.682614i	$0.239157\pi$
$822$	47456.0i	2.01365i
$823$	4472.00i	0.189410i	0.995505	+	0.0947048i	$0.0301907\pi$
$823$	4472.00i	0.189410i	−0.995505	+	0.0947048i	$0.969809\pi$
$824$	−6656.00	−0.281399
$825$	0	0
$826$	−2800.00	−0.117947
$827$	− 1716.00i	− 0.0721538i	−0.999349	−	0.0360769i	$-0.988514\pi$
$827$	− 1716.00i	− 0.0721538i	0.999349	−	0.0360769i	$-0.0114861\pi$
$828$	16576.0i	0.695720i
$829$	7910.00	0.331394	0.165697	−	0.986177i	$-0.447013\pi$
$829$	7910.00	0.331394	0.165697	+	0.986177i	$0.447013\pi$
$830$	0	0
$831$	42352.0	1.76796
$832$	1152.00i	0.0480029i
$833$	− 3626.00i	− 0.150820i
$834$	44800.0	1.86007
$835$	0	0
$836$	−8960.00	−0.370680
$837$	5760.00i	0.237867i
$838$	27120.0i	1.11795i
$839$	19360.0	0.796641	0.398320	−	0.917246i	$-0.369593\pi$
$839$	19360.0	0.796641	0.398320	+	0.917246i	$0.369593\pi$
$840$	0	0
$841$	11711.0	0.480175
$842$	1476.00i	0.0604113i
$843$	− 25936.0i	− 1.05965i
$844$	15472.0	0.631005
$845$	0	0
$846$	−1776.00	−0.0721751
$847$	3829.00i	0.155332i
$848$	− 5088.00i	− 0.206041i
$849$	12736.0	0.514839
$850$	0	0
$851$	38752.0	1.56099
$852$	12544.0i	0.504402i
$853$	− 698.000i	− 0.0280177i	−0.999902	−	0.0140088i	$-0.995541\pi$
$853$	− 698.000i	− 0.0280177i	0.999902	−	0.0140088i	$-0.00445930\pi$
$854$	2772.00	0.111072
$855$	0	0
$856$	−3552.00	−0.141828
$857$	− 23406.0i	− 0.932945i	−0.884536	−	0.466472i	$-0.845525\pi$
$857$	− 23406.0i	− 0.932945i	0.884536	−	0.466472i	$-0.154475\pi$
$858$	− 8064.00i	− 0.320863i
$859$	−7280.00	−0.289162	−0.144581	−	0.989493i	$-0.546183\pi$
$859$	−7280.00	−0.289162	−0.144581	+	0.989493i	$0.546183\pi$
$860$	0	0
$861$	−9072.00	−0.359086
$862$	− 2544.00i	− 0.100521i
$863$	− 9808.00i	− 0.386869i	−0.981113	−	0.193435i	$-0.938037\pi$
$863$	− 9808.00i	− 0.386869i	0.981113	−	0.193435i	$-0.0619627\pi$
$864$	2560.00	0.100802
$865$	0	0
$866$	10124.0	0.397260
$867$	4504.00i	0.176429i
$868$	2016.00i	0.0788335i
$869$	6720.00	0.262325
$870$	0	0
$871$	−12888.0	−0.501370
$872$	− 14960.0i	− 0.580974i
$873$	− 50098.0i	− 1.94222i
$874$	−17920.0	−0.693539
$875$	0	0
$876$	17216.0	0.664012
$877$	− 8066.00i	− 0.310570i	−0.987870	−	0.155285i	$-0.950370\pi$
$877$	− 8066.00i	− 0.310570i	0.987870	−	0.155285i	$-0.0496295\pi$
$878$	11280.0i	0.433578i
$879$	40176.0	1.54164
$880$	0	0
$881$	25842.0	0.988240	0.494120	−	0.869394i	$-0.335490\pi$
$881$	25842.0	0.988240	0.494120	+	0.869394i	$0.335490\pi$
$882$	− 3626.00i	− 0.138428i
$883$	5692.00i	0.216932i	0.994100	+	0.108466i	$0.0345939\pi$
$883$	5692.00i	0.216932i	−0.994100	+	0.108466i	$0.965406\pi$
$884$	−5328.00	−0.202715
$885$	0	0
$886$	−26776.0	−1.01530
$887$	− 13536.0i	− 0.512395i	−0.966624	−	0.256198i	$-0.917530\pi$
$887$	− 13536.0i	− 0.512395i	0.966624	−	0.256198i	$-0.0824698\pi$
$888$	− 22144.0i	− 0.836829i
$889$	13608.0	0.513383
$890$	0	0
$891$	10052.0	0.377951
$892$	15872.0i	0.595778i
$893$	− 1920.00i	− 0.0719489i
$894$	8160.00	0.305270
$895$	0	0
$896$	896.000	0.0334077
$897$	− 16128.0i	− 0.600332i
$898$	− 6460.00i	− 0.240059i
$899$	−13680.0	−0.507512
$900$	0	0
$901$	23532.0	0.870105
$902$	9072.00i	0.334883i
$903$	− 23072.0i	− 0.850264i
$904$	11024.0	0.405589
$905$	0	0
$906$	−9472.00	−0.347336
$907$	17004.0i	0.622501i	0.950328	+	0.311251i	$0.100748\pi$
$907$	17004.0i	0.622501i	−0.950328	+	0.311251i	$0.899252\pi$
$908$	15744.0i	0.575422i
$909$	50246.0	1.83339
$910$	0	0
$911$	−14568.0	−0.529813	−0.264906	−	0.964274i	$-0.585341\pi$
$911$	−14568.0	−0.529813	−0.264906	+	0.964274i	$0.585341\pi$
$912$	10240.0i	0.371799i
$913$	− 30016.0i	− 1.08804i
$914$	−21292.0	−0.770544
$915$	0	0
$916$	19240.0	0.694004
$917$	5936.00i	0.213767i
$918$	11840.0i	0.425684i
$919$	1400.00	0.0502522	0.0251261	−	0.999684i	$-0.492001\pi$
$919$	1400.00	0.0502522	0.0251261	+	0.999684i	$0.492001\pi$
$920$	0	0
$921$	−76288.0	−2.72940
$922$	− 14564.0i	− 0.520217i
$923$	− 7056.00i	− 0.251626i
$924$	−6272.00	−0.223305
$925$	0	0
$926$	−25376.0	−0.900548
$927$	− 30784.0i	− 1.09070i
$928$	6080.00i	0.215071i
$929$	13830.0	0.488426	0.244213	−	0.969722i	$-0.421470\pi$
$929$	13830.0	0.488426	0.244213	+	0.969722i	$0.421470\pi$
$930$	0	0
$931$	3920.00	0.137994
$932$	− 8728.00i	− 0.306754i
$933$	7744.00i	0.271733i
$934$	−5632.00	−0.197307
$935$	0	0
$936$	−5328.00	−0.186059
$937$	− 24166.0i	− 0.842549i	−0.906933	−	0.421275i	$-0.861583\pi$
$937$	− 24166.0i	− 0.842549i	0.906933	−	0.421275i	$-0.138417\pi$
$938$	10024.0i	0.348929i
$939$	−24464.0	−0.850216
$940$	0	0
$941$	−10838.0	−0.375461	−0.187730	−	0.982221i	$-0.560113\pi$
$941$	−10838.0	−0.375461	−0.187730	+	0.982221i	$0.560113\pi$
$942$	42976.0i	1.48645i
$943$	18144.0i	0.626564i
$944$	3200.00	0.110330
$945$	0	0
$946$	−23072.0	−0.792955
$947$	− 40916.0i	− 1.40400i	−0.712175	−	0.702002i	$-0.752290\pi$
$947$	− 40916.0i	− 1.40400i	0.712175	−	0.702002i	$-0.247710\pi$
$948$	− 7680.00i	− 0.263117i
$949$	−9684.00	−0.331250
$950$	0	0
$951$	−39888.0	−1.36010
$952$	4144.00i	0.141080i
$953$	− 56618.0i	− 1.92449i	−0.272189	−	0.962244i	$-0.587747\pi$
$953$	− 56618.0i	− 1.92449i	0.272189	−	0.962244i	$-0.412253\pi$
$954$	23532.0	0.798613
$955$	0	0
$956$	−12000.0	−0.405970
$957$	− 42560.0i	− 1.43759i
$958$	− 6320.00i	− 0.213142i
$959$	−20762.0	−0.699103
$960$	0	0
$961$	−24607.0	−0.825988
$962$	12456.0i	0.417461i
$963$	− 16428.0i	− 0.549725i
$964$	−8168.00	−0.272898
$965$	0	0
$966$	−12544.0	−0.417802
$967$	17504.0i	0.582100i	0.956708	+	0.291050i	$0.0940046\pi$
$967$	17504.0i	0.582100i	−0.956708	+	0.291050i	$0.905995\pi$
$968$	− 4376.00i	− 0.145300i
$969$	−47360.0	−1.57010
$970$	0	0
$971$	23112.0	0.763851	0.381926	−	0.924193i	$-0.375261\pi$
$971$	23112.0	0.763851	0.381926	+	0.924193i	$0.375261\pi$
$972$	− 20128.0i	− 0.664204i
$973$	19600.0i	0.645783i
$974$	−28352.0	−0.932707
$975$	0	0
$976$	−3168.00	−0.103899
$977$	23874.0i	0.781778i	0.920438	+	0.390889i	$0.127832\pi$
$977$	23874.0i	0.781778i	−0.920438	+	0.390889i	$0.872168\pi$
$978$	− 16192.0i	− 0.529410i
$979$	22680.0	0.740404
$980$	0	0
$981$	69190.0	2.25185
$982$	22536.0i	0.732335i
$983$	15312.0i	0.496823i	0.968655	+	0.248411i	$0.0799085\pi$
$983$	15312.0i	0.496823i	−0.968655	+	0.248411i	$0.920091\pi$
$984$	10368.0	0.335894
$985$	0	0
$986$	−28120.0	−0.908239
$987$	− 1344.00i	− 0.0433435i
$988$	− 5760.00i	− 0.185476i
$989$	−46144.0	−1.48361
$990$	0	0
$991$	−16528.0	−0.529797	−0.264899	−	0.964276i	$-0.585339\pi$
$991$	−16528.0	−0.529797	−0.264899	+	0.964276i	$0.585339\pi$
$992$	− 2304.00i	− 0.0737420i
$993$	− 68896.0i	− 2.20176i
$994$	−5488.00	−0.175120
$995$	0	0
$996$	−34304.0	−1.09133
$997$	− 28606.0i	− 0.908687i	−0.890827	−	0.454344i	$-0.849874\pi$
$997$	− 28606.0i	− 0.908687i	0.890827	−	0.454344i	$-0.150126\pi$
$998$	− 8920.00i	− 0.282924i
$999$	27680.0	0.876633

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	350.4.c.b.99.1		2
5.2	odd	4		350.4.a.l.1.1		1
5.3	odd	4		14.4.a.a.1.1	✓	1
5.4	even	2	inner	350.4.c.b.99.2		2
15.8	even	4		126.4.a.h.1.1		1
20.3	even	4		112.4.a.a.1.1		1
35.3	even	12		98.4.c.f.79.1		2
35.13	even	4		98.4.a.a.1.1		1
35.18	odd	12		98.4.c.d.79.1		2
35.23	odd	12		98.4.c.d.67.1		2
35.27	even	4		2450.4.a.bo.1.1		1
35.33	even	12		98.4.c.f.67.1		2
40.3	even	4		448.4.a.o.1.1		1
40.13	odd	4		448.4.a.b.1.1		1
55.43	even	4		1694.4.a.g.1.1		1
60.23	odd	4		1008.4.a.s.1.1		1
65.38	odd	4		2366.4.a.h.1.1		1
105.23	even	12		882.4.g.b.361.1		2
105.38	odd	12		882.4.g.k.667.1		2
105.53	even	12		882.4.g.b.667.1		2
105.68	odd	12		882.4.g.k.361.1		2
105.83	odd	4		882.4.a.i.1.1		1
140.83	odd	4		784.4.a.s.1.1		1

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
14.4.a.a.1.1	✓	1	5.3	odd	4
98.4.a.a.1.1		1	35.13	even	4
98.4.c.d.67.1		2	35.23	odd	12
98.4.c.d.79.1		2	35.18	odd	12
98.4.c.f.67.1		2	35.33	even	12
98.4.c.f.79.1		2	35.3	even	12
112.4.a.a.1.1		1	20.3	even	4
126.4.a.h.1.1		1	15.8	even	4
350.4.a.l.1.1		1	5.2	odd	4
350.4.c.b.99.1		2	1.1	even	1	trivial
350.4.c.b.99.2		2	5.4	even	2	inner
448.4.a.b.1.1		1	40.13	odd	4
448.4.a.o.1.1		1	40.3	even	4
784.4.a.s.1.1		1	140.83	odd	4
882.4.a.i.1.1		1	105.83	odd	4
882.4.g.b.361.1		2	105.23	even	12
882.4.g.b.667.1		2	105.53	even	12
882.4.g.k.361.1		2	105.68	odd	12
882.4.g.k.667.1		2	105.38	odd	12
1008.4.a.s.1.1		1	60.23	odd	4
1694.4.a.g.1.1		1	55.43	even	4
2366.4.a.h.1.1		1	65.38	odd	4
2450.4.a.bo.1.1		1	35.27	even	4

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 350 = 2 \cdot 5^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	350.c (of order \(2\), degree \(1\), not minimal)

\(f(q)\)	\(=\)	\(q-2.00000i q^{2} -8.00000i q^{3} -4.00000 q^{4} -16.0000 q^{6} -7.00000i q^{7} +8.00000i q^{8} -37.0000 q^{9} +O(q^{10})\)	\(q-2.00000i q^{2} -8.00000i q^{3} -4.00000 q^{4} -16.0000 q^{6} -7.00000i q^{7} +8.00000i q^{8} -37.0000 q^{9} -28.0000 q^{11} +32.0000i q^{12} -18.0000i q^{13} -14.0000 q^{14} +16.0000 q^{16} +74.0000i q^{17} +74.0000i q^{18} -80.0000 q^{19} -56.0000 q^{21} +56.0000i q^{22} +112.000i q^{23} +64.0000 q^{24} -36.0000 q^{26} +80.0000i q^{27} +28.0000i q^{28} -190.000 q^{29} +72.0000 q^{31} -32.0000i q^{32} +224.000i q^{33} +148.000 q^{34} +148.000 q^{36} -346.000i q^{37} +160.000i q^{38} -144.000 q^{39} +162.000 q^{41} +112.000i q^{42} +412.000i q^{43} +112.000 q^{44} +224.000 q^{46} +24.0000i q^{47} -128.000i q^{48} -49.0000 q^{49} +592.000 q^{51} +72.0000i q^{52} -318.000i q^{53} +160.000 q^{54} +56.0000 q^{56} +640.000i q^{57} +380.000i q^{58} +200.000 q^{59} -198.000 q^{61} -144.000i q^{62} +259.000i q^{63} -64.0000 q^{64} +448.000 q^{66} -716.000i q^{67} -296.000i q^{68} +896.000 q^{69} +392.000 q^{71} -296.000i q^{72} -538.000i q^{73} -692.000 q^{74} +320.000 q^{76} +196.000i q^{77} +288.000i q^{78} -240.000 q^{79} -359.000 q^{81} -324.000i q^{82} +1072.00i q^{83} +224.000 q^{84} +824.000 q^{86} +1520.00i q^{87} -224.000i q^{88} -810.000 q^{89} -126.000 q^{91} -448.000i q^{92} -576.000i q^{93} +48.0000 q^{94} -256.000 q^{96} +1354.00i q^{97} +98.0000i q^{98} +1036.00 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q - 8 q^{4} - 32 q^{6} - 74 q^{9}+O(q^{10}) \) 2 * q - 8 * q^4 - 32 * q^6 - 74 * q^9	\( 2 q - 8 q^{4} - 32 q^{6} - 74 q^{9} - 56 q^{11} - 28 q^{14} + 32 q^{16} - 160 q^{19} - 112 q^{21} + 128 q^{24} - 72 q^{26} - 380 q^{29} + 144 q^{31} + 296 q^{34} + 296 q^{36} - 288 q^{39} + 324 q^{41} + 224 q^{44} + 448 q^{46} - 98 q^{49} + 1184 q^{51} + 320 q^{54} + 112 q^{56} + 400 q^{59} - 396 q^{61} - 128 q^{64} + 896 q^{66} + 1792 q^{69} + 784 q^{71} - 1384 q^{74} + 640 q^{76} - 480 q^{79} - 718 q^{81} + 448 q^{84} + 1648 q^{86} - 1620 q^{89} - 252 q^{91} + 96 q^{94} - 512 q^{96} + 2072 q^{99}+O(q^{100}) \) 2 * q - 8 * q^4 - 32 * q^6 - 74 * q^9 - 56 * q^11 - 28 * q^14 + 32 * q^16 - 160 * q^19 - 112 * q^21 + 128 * q^24 - 72 * q^26 - 380 * q^29 + 144 * q^31 + 296 * q^34 + 296 * q^36 - 288 * q^39 + 324 * q^41 + 224 * q^44 + 448 * q^46 - 98 * q^49 + 1184 * q^51 + 320 * q^54 + 112 * q^56 + 400 * q^59 - 396 * q^61 - 128 * q^64 + 896 * q^66 + 1792 * q^69 + 784 * q^71 - 1384 * q^74 + 640 * q^76 - 480 * q^79 - 718 * q^81 + 448 * q^84 + 1648 * q^86 - 1620 * q^89 - 252 * q^91 + 96 * q^94 - 512 * q^96 + 2072 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more